A consequence of Einsten's Theories of Relativity is that mass is not constant with velocity -- the mass of a body is the 'rest mass' (some constant) multiplied by one over the square root of (1 - (v/c)^2) -- in other words, if a body is moving its mass increases, until as the speed approaches 'c' (the speed of light), the mass tends to infinity, because you end up trying to divide by zero.
Therefore, if we apply F = ma (Newton); or more correctly,F = d(mv)/dt, we have that for constant force, the acceleration will tend asymptotically to zero as v tends to 'c'. Or, if you like, you can push your body as hard as you like for as long as you like but the acceleration will still tend to zero.
For a wonderfully simple explanation of this sort of thing, try Richard Feynman's 'Six Not-So-Easy Pieces' (which, despite the title, are remarkably straightforward) --
http://www.amazon.co.uk/exec/obidos/...868995-7395022.